arXiv
Open Access
2025
A Characterization of Functional Affine Surface Areas
Fernanda M. Baêta
Abstrak
A characterization of valuations on the space of convex Lipschitz functions whose domain is a polytope in $\mathbb{R}^n$ is obtained. It is shown that every upper semicontinuous, equi-affine and dually epi-translation invariant valuation can be written as a linear combination of a constant term, the volume of the domain, and a functional affine surface area. In addition, dual statements for finite-valued convex functions are established.
Penulis (1)
F
Fernanda M. Baêta
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2025
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- en
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- Open Access ✓